/sci/ - Science & Math

sage

>>5329036
0/10
/thread

>>5329060
>>5329069
This doesn't seem like that bad of an argument. Anyways, I always figured that it was all just an error in our notation, but mathfags seem to think it's more than that.

(1/3)*3=1
1/3=.333... .333...*3=.999.......

^^^so... it's a quirk of decimal notation, basically. yes?

But then there's the argument that, by definition, .999... approaches 1 so closely that it's indistinguishable from one, basically, yes? So that's sort of the same thing as I was saying before. But then it points out the fact that numbers are just in our heads, I guess... and everything is everything and everything is one, and numberless, so to speak.

Can someone point out all the parts where I'm wrong, or just call me a faggot and go back to playing vidya? Thanks, that would be great.

i guess .000...01 times infinity equals zero, also. because the 1 never comes.

>>5329089
>>5329089
>1/3=.333... .333...
No.
0.333... < 1/3

Of course all the mathfags think 1/3 = 0.333333..
Because it's circular reasoning from 0.999... = 1.
They have been brainwashed, they're wrong.

It doesn't make sense for 1/3 to be just a series of 3.
And it doesn't make sense for 1 to be a series of 9.

>>5329105
Yes you could say so but 0,0...01 doesn't really exist

>>5329116
right, and neither does .999...

>>5329036

>>5329120
>Only argument is a literally meaningless phrase

http://en.wikipedia.org/wiki/0.999...#Dedekind_cuts

>>5329134

ITT: Nonmathfags who think they know math better than everyone else

http://en.wikipedia.org/wiki/Infinite_(cardinality)

>>5329134
>Orange rectangle
Throw a coin on an infinite plane.
It will fall on point P.
Scenario A (what they want you to believe):
The probability of the coin falling on P is 0 (1/inf = 0).
It can't fall on P. A coin can't fall on an infinite plane. Yet it will.
Scenario B (the truth):
The probability of the coin falling on P is an infinitely small number.
So infinitely small numbers have to exist, at least conceptually.

>Green rectangle
Already talked about the mistake, 10*0.999 = 9.990 != 9.999, so 10*0.999... != 9.999...
At the very best, it's circular reasoning.

>Brown rectangle
>1/3 = 0.333...
No. Circular reasoning, appeal to stupidity.

>Blue rectangle
The demonstration of the "convergence theorem" relies on infinitely small numbers being approximated to 0. r^x = 0 when 0<r<1 and x->infinity. See wikipedia. Circular reasoning.

>>5329134
ooh i really like that geometric series one

>babby's first troll attempt
how cute :3

>>5329161
>10*0.999 = 9.990 != 9.999, so 10*0.999... != 9.999...

I don't think you understand infinity. The cardinality of {0.9, 0.09, 0.009, ...} is the same as {9, 0.9, 0.09, 0.009, ...}.

You seem to believe that the 1 - 0.999... = 0.000...01. This implies that there is a smallest interval in the real numbers, which is demonstrably false.

ITT: Op doesn't understand elipsis notation.

>>5329220
I understand it and dismiss it as sophism.
When people discuss 0.999... = 1, they mean 0.99999..., not the limit of its construction.

>>5329214
>You seem to believe that the 1 - 0.999... = 0.000...01
It would be true if reals were finite like a deck of cards.
But between A and B, there is an infinite number of cards. It is weird.
And you need to understand that weirdness to see that 1 - 0.999... is not really a number, but a concept.
0.999... too, is not really a number. Because infinity doesn't really exist. It is a concept disguised as a number.
0.999... is infinitely close to 1 but it does not make logical sense to have something static infinitely close yet different.
And 0.00..1 does not make sense as a number because you could divide it by 2. Yet the infinitesimal has to exist in the abstract.
The numeral system is messed up, bullshit all over the place.

>>5329220
Ellipsis notation is unmathematical and lacking rigor.

>>5329276
Addendum: This is why modern maths dismiss the infinitesimal, and approximate it as 0. Because the only way to get correct results is to forsake the infinity which doesn't actually exist and introduces wrongness in the equations.

>>5329281
It isn't, if reals are rejected as the obvious bullshit they are. Then it can be given quite a firm meaning.

Ok then, op
What is the number in between .99999... and 1?

>>5329316

For two distinct numbers x and y the number (x+y)/2 is between them.

>>5329319
And what is (.99999... + 1)/2?

or, what is 1 - .999999?

>>5329320
sorry, I meant .9999...

>>5329320
What do you mean? It's a number. The reals are closed under addition and multiplicaiton.

Alright listen up tard nuggets.

The argument saying 0.99999... =/= 1 is ridiculous because it assumes that every element in the decimal system is expressed uniquely.

0.999... and 1 are just a different way of expressing the same value.

>>5329324
What is 1-.999...

>>5329324
Right, it is a real number, and that number is 1
(1+1)/2 is 1.

>>5329325
What are you asking? For two real numbers x and y the number x-y is another real number.

>>5329328
The expression wasn't (1+1)/2. It was (1+0.999...)/2

>>5329334
So, then the expression what (1+1)/2, since those are just different ways of expressing the same number

>>5329327
>different way of expressing the same value.

What's a value?

>>5329338
Then you are committing the fallacy of circular reasoning.

>>5329345
No, I'm committing the fallacy of telling you that .9999... = 1

>>5329347
So you admit it is a fallacy?

>>5329347
You are free to tell me that 0.999... equals 1 and I agree with you. But you clearly don't understand why they are equal. You accepted it as an obscure fact, but YOU aren't able to prove it.

>>5329351
No, I was joking because you don't seem to understand what a fallacy is.

>>5329354
Does that matter?

>>5329324
> the reals exist
sure they do, bud, sure they do

>>5329339
A value is an analogical thing. It can be anything. A value of dollars, a value of chickens, etc.
Numbers and decimals are just symbolic representations of analogical things.

>>5329358
It does. If you don't understand the mathematical background, you are not entitled to spout your pseudo-intellectual middle schooler drivel in a math thread.

>>5329363
I'm pretty sure I'm entitled to spout whatever I want.

But that's the extent of why it matters to you? participation in a 4chan thread?

This trollpost doesn't even make me mad anymore. Take calc 2, please. This is a simple geometric series.
.999...=9/10+9/100+9/1000...=http://www.wolframalpha.com/input/?i=summation+from+1+to+infinity+of+9%
281%2F10%29%5En

>>5329361
Then show me a negative number of chickens. Or an imaginary number of dollars.

>>5329366
Why do you oppose education?

Another "0.(9)=!=1" thread
>35 posts and 4 image replies omitted

Shit /sci/rone, get it together.

>>5329373
Wait, so this is about education? Because when I asked you why it mattered, you gave me the above response.

Your mistake is that the nines don't end. There is no . . .0001 at the end, because infinity isn't just some really big number.

>>5329376
It is about your education. You are lacking education and instead of learning you shitpost.

>>5329368
I have a feeling I am being trolled. Anyways. A negative amount would be the symbolic representation of debt (which has an analogical meaning).
Your question is equivalent to "show me i dollars."

>>5329380
I have a law school education.

It's a social thing.

>>5329105
Infinity is not a number and I don't think that 0.00...01 is either. Also, in limits 0 times "infinity" is not always 0.
In fact, I think your thing would be one
lim_x->infty (1/x)*x=1


By the way, 0.999... doesn't _approach_ one or become infinitely close to it; it's a number and doesn't approach anything, though it is equal to one.

>>5329381
You said a value has to be an "analogical thing". A symbolic representation doesn't make sense without an "analogical thing". Show me a negative or an imaginary "analogical thing".

>>5329389
>Infinity is not a number

You are so fucking retarded. Please kill yourself. Infinity is a number, it's just not a REAL number.

>>5329120
the ellipsis does _not_ mean "a ton of but finite number of 3s."

>>5329396
The ellipsis can mean anything. It's ambiguous and unrigorous notation.

>>5329120
>It doesn't make sense for 1/3 to be just a series of 3.
>And it doesn't make sense for 1 to be a series of 9.
What do you mean by these?
It doesn't make sense for people to write these numbers these ways?

>>5329390
Yep, I'm being trolled. Not like I have anything better to do though.
>You said a value has to be an "analogical thing"
I never said it has to, only that it can. Mathematics at it's core is just a bunch of axioms invented (or discovered as some might say) to do the above.
Either way this has nothing to do with the 0.999... debate because it does not change the fact that decimals are not unique.

>>5329409
You were talking about the "value" of a number. I was asking you what "value" means mathematically. Can you answer the question or were you just talking out of your ass?

>>5329395
>Infinity is a number

>>5329412
Define "number". Do you really think the reals are the only numbers? Go back to your middle school math class and have fun solving linear equations.

>>5329411
>You were talking about the "value" of a number
Yes. Mathematically, the definition of value is the output of a function (google dat shit). In layman terms it is how much of something. If you want to use technical terms then by all means I' could rephrase my sentence, but if you are educated enough to understand it, you should be educated enough to know what I meant by value and you should definitely be educated enough to know 1 = 0.999...

>>5329425
I don't want layman terms. Put it down mathematically. I have a degree in math and I never encountered a definition of "value".

>>5329400
1/3 = 10/30 = 9/3 + 1/30 = 0.3 + 1/30 = 0.3 + 0.03 + 0.003 + 0.0003 + ... 1/(3*10^n)
>1/(3*10^n)
That last term becomes infinitesimal when the number of addition is infinity.
And when you say 1/3 is just a series of 3, you discard that last term.
But as I said, you can't just act as the infinitesimal doesn't exist.
Otherwise, you can't land a coin on an infinite plane. >>5329161
This is why it is obvious that 1/3 can't be written as a series of 3.
It does not want to. It is not its true nature.

Once you try to state that 1 isn't equal to 0.999..., you open a huge can of worms for yourself, starting with 1/3 not equaling 0.333... and the fallibility of real numbers. Furthermore, there's there whole "no infinity" argument, which also eliminates pi. Then they say that nobody can actually measure pi (which explains why we have 1 million + digits of it), so it doesn't exist. Really, you cannot- literally CANNOT- say that 1 is not 0.999... without breaking all of mathematics.

>>5329430
>I have a degree in math
Then why the fuck are you asking me such stupid shit?

"The argument for 0.999... =/= 1 is ridiculous because it assumes that every number in the decimal system is unique. That is, a number cannot be expressed in any other form."

Simply stated, 0.9999999 and 1 are a different way of expressing the same number.

>>5329425
>being educated enough to swallow dogma without questioning it
I seriously hope you guys don't do this.

>>5329456
I am interested in learning new mathematical definitions and their implications. Can you please point me to any source? You claimed to have a definition for "value".

>>5329439
The problem with pi is that perfect circles can't exist.
And pi is the ratio circumference/diameter of a perfect circle.

I hate real numbers.

>>5329438
>1/3 = 10/30 = 9/3 + 1/30
lol wut

>>5329438
There is no last term

>>5329467
Oh fuck off, I used value as lay term. I have yet to hear a counter argument to the edited statement. If you want a formal definition for value you can google that yourself. Also, arguing over semantics doesn't make you cool.

>>5329484
there's nothing to hate, they're just absolutely retarded bullshit
> hey guys let's solve this problem
ok
> I need an infinite amount of numbers
ok...
> actually lol I need another infinite amount, but don't worry, they're the same "size"
umm
> whoops I need another infinity, but don't worry, this one is no bigger than the last
listen, um
> oh did I imply I was done? I'm sorry. I actually need an infinite number of infinities. Sorry, this one is really big but I promise it's the last
I don't think that---
> hmm, that's weird. I can't even define most of them.
Doesn't that seem like a---
> weirder yet, I can't even NAME them all
---problem? I mean
> oh well! I'm sure it makes sense
YOU'RE FUCKING RETARDED

The question is whether we can consider A=B if A is an infinitely close approximation of B. I don't think we actually can, or if fucks with how infinitesimals work. If A=B when A is simply infinitely close to be, than 0=An infinitesimal. This would seriously fuck up calculus, among other things.

It's better to say 1-.99999...=An infinitesimal. The problem comes here is that base ten can't represent 1/3 at all, it can only infinitely approximate it.

>>5329471
In mathematics perfect circles exist, and in mathematics 0.999..... = 1. Please fuck off with your bullshit.

>>5329495
Go read Cantor's proofs and shut the fuck up, pleb.

>>5329493
Why do you use layman terms in a math thread? Is it because you lack the mathematical education to prove the statement in a clean and rigorous manner?

>>5329496
> needs an infinite number of infinite numbers of infinite numbers of infinite numbers
> but 0.999... is the problem
god damn it what is wrong with you people, you can't even fucking solve representation problems without bringing up even more fucking infinities

This addiction to infinities needs to fucking stop. I will grant you countable sets---that's it. You want more, too fucking bad.

>>5329500
I can't get through them because when I try to work with infinities I can never finish any of the steps.

>>5329508
>>5329512
Infinity can fit an infinite amount of infinities within itself. It can in turn be thought of as being able to fit within some other, greater infinity.

That's all intuitively obvious, really.

>>5329501
>internet imageboard created for anime nerds
>rigour
If you want rigour, go to a lecture.
Also, nice subtle ad hominem there.
Still no counter argument.
anyways 4/10 for making me reply so many times, play again later.

>>5329525
Where's your reading comprehension? Why do you expect me to come up with an argument? I am not arguing anything. I was just asking you a question. And no, this is not an anime board. This is the science and math board. Math is to be discussed rigorously.

>>5329537
>This is the science and math board. Math is to be discussed rigorously.

>>5329542
Do not post off-topic image macros. Shitposting belongs on >>>/sp/

>>5329547

>>5329547
Who are you?

>>5329399
No, it has a very well defined meaning in matheamtics. It means never-ending if nothing is written after it, and continuing by a given pattern if there is something written after it, ex:

1, 3, 5, 7, ... , 27, 29, 31.

>>5329560
I am Anonymous.

>>5329561
That's not a rigorous way of defining a pattern. You could put anything there for the ellipsis.

>>5329561
>It means never-ending if nothing is written after it

It doesn't equal 1. All of the proofs posted here are invalid.

>>5329562

>>5329597